Sequences & Series — A-Level Mathematics Revision
Revise Sequences & Series for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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- Sequences & Series in A-Level Mathematics: explanation, examples, and practice links on this page.
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Go to TrigonometryWhat is Sequences & Series?
Sequences and series at A-Level Maths deal with arithmetic and geometric progressions. You'll learn to find the nth term, the sum of the first n terms, and the sum to infinity for geometric series where applicable. This topic is foundational for understanding calculus and other areas of mathematics.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover both arithmetic and geometric sequences and series. The notation and complexity of problems may vary slightly, but the core concepts are the same.
Step-by-step explanationWorked example
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ... The first term a = 2 and the common ratio r = 6/2 = 3. The sum of the first n terms is given by Sn = a(r^n - 1) / (r - 1). So, S10 = 2(3^10 - 1) / (3 - 1) = 3^10 - 1 = 59048.
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Common mistakes
- 1Confusing the formulae for arithmetic and geometric sequences. It's crucial to identify whether a sequence has a common difference (arithmetic) or a common ratio (geometric).
- 2Incorrectly using the sum to infinity formula. This formula only applies to geometric series where the absolute value of the common ratio |r| is less than 1.
- 3Making errors with sigma notation. Understanding how to correctly interpret the limits of the summation and the expression being summed is key.
Sequences & Series exam questions
Exam-style questions for Sequences & Series with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Sequences & Series
Core concept
Sequences and series at A-Level Maths deal with arithmetic and geometric progressions. You'll learn to find the nth term, the sum of the first n terms, and the sum to infinity for geometric series whe…
Frequently asked questions
What is the difference between a sequence and a series?
A sequence is a list of numbers in a specific order, while a series is the sum of the terms of a sequence.
When can I use the sum to infinity formula?
The sum to infinity formula can only be used for a geometric series when the common ratio r is between -1 and 1 (i.e., |r| < 1).